Date: Tue, 26 Nov 1996 00:11:22 GMT
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<html> <head><title>Courant Mathematics and Computing Laboratory </title>
<Center><H1>Courant Mathematics and Computing Laboratory </H1>  </Center>
<Center><H3><I>supported by the 
<!WA0><A HREF="http://www.doe.gov/html/home.html"> Department of Energy</A></I></H3></Center>
</head>
<body>

<hr>
<Center><H2> Computational Mathematics and Applied Analysis
</H2></Center>
<hr>

<H2>Overview</H2>

The Courant Mathematics and Computing Laboratory (CMCL)
is a research center at the Courant Institute of New York University.
Our program is devoted to 
the formulation, analysis and numerical resolution
of a broad class of scientific problems, drawn from aerodynamics,
multi-phase flow, combustion, electromagnetic theory, nonlinear optics
and materials science. One component of the CMCL involves the design of
new schemes for partial differential equations,
particularly those which support adaptive mesh refinement, fast
algorithms, and parallel computation.
A second component of our
effort concerns the modeling and numerical investigation of a variety
of questions in materials science, interface motion, and nonlinear
optics.
The third component of the CMCL
involves the mathematical analysis of the phenomenology of nonlinear
conservation laws and incompressible flow.

<P>
<H2>People</H2>

<P> The research personnel of the CMCL consists of 7 faculty members,
9 graduate students, and several postdoctoral fellows. 
The current members include:</P>

<ul>

<li> Principal Investigators

<dl>  
<dd><!WA1><A HREF="http://www.math.nyu.edu/faculty/lax/index.html">Peter Lax </a>
<dd><!WA2><A HREF="http://cs.nyu.edu/cs/faculty/berger/index.html">Marsha Berger </a>
<dd><!WA3><A HREF="http://www.math.nyu.edu/faculty/greengar/index.html">Leslie 
Greengard </a>
     </dl>
<li> Faculty
<dl>  
<dd><!WA4><A HREF="http://cs.nyu.edu/cs/faculty/greenbau/index.html">Anne 
Greenbaum </a>
<dd><!WA5><A HREF="http://www.math.nyu.edu/faculty/muraki/index.html">Dave
Muraki </a>
<dd><!WA6><A HREF="http://www.math.nyu.edu/faculty/shelley/index.html">Michael
Shelley </a>
<dd><!WA7><A HREF="http://www.math.nyu.edu/faculty/xin/index.html">Zhouping
Xin </a>
     </dl>
<li> Postdocs
<dl>  
<dd> Lou Kondic </a>
<dd> Xu-dong Liu </a>
<dd> <!WA8><A HREF = "http://math.nyu.edu/postdocs/minion/index.html">Michael Minion </a>
     </dl>

</ul>

<H2>Principal Research Projects</H2>
This is a partial listing of some of our projects.

<ul>
<li>
<!WA9><A HREF="http://cs.nyu.edu/cs/faculty/berger/geom.html">
Numerical Simulation of Partial Differential Equations in Complex Geometry. </a>
</li>

<li>
<!WA10><A HREF="http://math.nyu.edu/faculty/shelley/kelvin/kelvin.html">
Interface motion under surface tension. </a>
</li>

<li>
Fast Algorithms and Iterative Methods. 
</li>

<li>
Discretization Schemes. 
</li>

<li>
Materials Science and Nonlinear Optics. 
</li>


<li>
<!WA11><A HREF = "http://math.nyu.edu/faculty/greengar/poisson.html">
A Fast Poisson Solver for Complex Geometries. </a>
</li>

<li>
<!WA12><A HREF="http://math.nyu.edu/postdocs/minion/res/under.html">
Spurious vorticies in underresolved incompressible flow calculations. </a>
</li>

<li>
<!WA13><A HREF="http://math.nyu.edu/postdocs/minion/res/bubble.html">
Investigation of singularities in Boussinesq convection. </a>
</li>

<li>
<!WA14><A HREF="http://cs.nyu.edu/cs/faculty/berger/ton.html">
Adaptive simulation of compressible reacting flows:
a study of laser induced spark ignition. </a>
</li>


</ul>

<H2>Software </H2>

The following software can be obtained via email from the contact person listed 
below. 

<ul>

<P>
<li> FMM: An adaptive 2-D Fast Multipole Method for Coulomb interactions
     is available from Leslie Greengard (greengard@cims.nyu.edu).
</P>

<P>
<li> AMR2D: An adaptive 2-D Adaptive Mesh Refinement code for hyperbolic
     conservation laws is available from Marsha Berger (berger@cims.nyu.edu).
</P>

<P>
<li> AMRCLAW: An adaptive version of R. LeVeque's 2-D CLAWPACK code is available
     from Marsha Berger (berger@cims.nyu.edu).
</P>

</ul>

<H2>Recent Postdoctoral Fellows Supported in part by the DOE </H2>
(under construction)

<TABLE BORDER>
	<TR>
		<TH>Name</TH>
		<TH>Research Area </TH>
		<TH>1st Position (after NYU)</TH>
		<TH>Employer</TH>
	</TR>


	<TR>
		<TH>S. Karni</TH>
		<TH>Comp. Fluid Dynamics </TH>
		<TH>Asst. Prof.</TH>
		<TH>Temple University</TH>
	</TR>

	<TR>
		<TH>V. Ton</TH>
		<TH>Comp. Fluid Dynamics </TH>
		<TH>Staff Scientist</TH>
		<TH>Aerospace Corp.</TH>
	</TR>
	<TR>
		<TH>R. Young</TH>
		<TH>Applied Analysis </TH>
		<TH>Postdoc </TH>
		<TH>Stonybrook </TH>
	</TR>
	<TR>
		<TH>D. Sidilkover</TH>
		<TH>Comp. Fluid Dynamics </TH>
		<TH>Staff Scientist</TH>
		<TH>ICASE </TH>
	</TR>
	<TR>
		<TH>M. Ward</TH>
		<TH>Applied Math. </TH>
		<TH>Asst. Prof. </TH>
		<TH>U.B.C. </TH>
	</TR>
	<TR>
		<TH>C. Liu </TH>
		<TH>Num. Analysis . </TH>
		<TH>Asst. Prof. </TH>
		<TH>U.S.C. </TH>
	</TR>
	<TR>
		<TH>R. Almgren </TH>
		<TH>Applied Math. </TH>
		<TH>Asst. Prof. </TH>
		<TH>U. Chicago </TH>
	</TR>
	<TR>
		<TH>A. Szepessy </TH>
		<TH>Applied & Num. Analysis </TH>
		<TH> Asst. Prof. </TH>
		<TH>K.T.H., Sweden</TH>
	</TR>
	<TR>
		<TH>R. Krasny </TH>
		<TH>Num. Analysis </TH>
		<TH> Asst. Prof. </TH>
		<TH>Univ. Michigan </TH>
	</TR>
	<TR>
		<TH>G. Russo </TH>
		<TH>Num. Analysis </TH>
		<TH> Asst. Prof. </TH>
		<TH>Italy</TH>
	</TR>


</TABLE>


<H2>Recent Ph.D. Theses Supported in part by the DOE </H2>
<TABLE BORDER>
	<TR>
		<TH>Name</TH>
		<TH>Thesis Title</TH>
		<TH>Ph.D. Year</TH>
		<TH>Adviser</TH>
		<TH>Employer</TH>
	</TR>

	<TR>
		<TH>H. Cheng</TH>
		<TH>A Method of Images for the Evaluation of
		Electrostatic Fields in Systems of Closely-Spaced
		Cylinders </TH>
		<TH>1995</TH>
		<TH>Greengard</TH>
		<TH>Princeton University</TH>
	</TR>
	<TR>
		<TH>A. Roma</TH>
		<TH>A Multilevel Self Adaptive Version of the Immersed
		Boundary Method </TH>
		<TH>1995</TH>
		<TH>Berger</TH>
		<TH>Univ. of Brazil</TH>
	</TR>
	<TR>
		<TH>M. Teytel</TH>
		<TH>Degeneracies in  Spectra of Linear Self-Adjoint
		Operators</TH>
		<TH>1996</TH>
		<TH>Lax</TH>
		<TH>Univ. of Penn. </TH>
	</TR>

	<TR>
		<TH>Min Chen</TH>
		<TH> Velocity Formulation of the Euler Eqs. and
		Symplectic Integration </TH>
		<TH>1996</TH>
		<TH>Lax</TH>
		<TH> </TH>
	</TR>
	<TR>
		<TH>J.-Y. Lee </TH>
		<TH>Singular Perturbation Problems </TH>
		<TH>1994</TH>
		<TH>Greengard</TH>
		<TH> Korea  </TH>
	</TR>
	<TR>
		<TH>Shlomo Engelberg</TH>
		<TH> On the stability of Certain classes of Solutions of
		the Burgers' eq. with Higher Order Viscosity </TH>
		<TH>1994</TH>
		<TH>Lax and Goodman</TH>
		<TH>Tel Aviv Univ.</TH>
	</TR>
	<TR>
		<TH>Brian Hayes </TH>
		<TH> (I) Stability of Solns. to a Destabilized Hopf eq.
		(II) Studies of the Kac-Mvan Moerbeke Lattice </TH>
		<TH>1994</TH>
		<TH>Lax </TH>
		<TH>U.S.C.</TH>
	</TR>
	<TR>
		<TH>Feiran Tian</TH>
		<TH>  Oscillations of the Zero Dispersion Limit of the
		Korteweg-de-Vries eq.  </TH>
		<TH>1991</TH>
		<TH>Lax </TH>
		<TH>Ohio State Univ.</TH>
	</TR>
	<TR>
		<TH>Sebastian Noelle</TH>
		<TH>  Cauchy Problems for the Complex Burgers Eq. in One
		and Two Space Dimensions</TH>
		<TH>1990</TH>
		<TH>Lax </TH>
		<TH>Univ. of Bonn</TH>
	</TR>
</TABLE>


